Lessing presents us with quite a complex picture of the relationship between the mother and son which is well worth thinking about in greater depth to understand the various dynamics that are in operation. Consider what background information we are given about Jerry and his mother:
She was thinking, Of course he's old enough to be safe without me. Have I been keeping him too close? He mustn't feel he ought to be with me. I must be careful.
He was an only child, eleven years old. She was a widow. She was determined to be neither possessive nor lacking in devotion. She went worrying off to her beach.
Here we can see the mother's internal conflict about letting Jerry go and his growing up, and the (normal) paranoia that parent's face in such matters. And yet, the fact that it is her alone bringing Jerry up and her "determination" hints at a kind of paranoia about being a good mother.
Let us now examine why Jerry decides to follow his mother to the "safe beach" on the first day:
He was very familiar with that anxious, apologetic smile. Contrition sent him running after her. And yet, as he ran, he looked back over his shoulder at the wild bay; and all morning, as he played on the safe beach, he was thinking of it.
Here we see that it was a sense of guilt that sent him to the safe beach with his mother. He is a boy that obviously feels he needs to protect his mother in some way, probably because she is a widower, and he doesn't want to put her through any more worry or pain or suffering. Yet, at the same time, he feels the attraction of the "wild bay," and the next day makes his break.